Romanian Statistical Review - Supplement nr. 2 / 2019114
A STRUCTURAL VISION OF THE ABSORPTION OF EUROPEAN FUNDS,
WHICH CORRELATES THE MONTE CARLO SIMULATION METHOD WITH THE SOLVER
METHOD
Ec. Ligian Tudoroiu
University of CraiovaProfessor habil. Gheorghe Săvoiu, PhDUniversity of Piteşti
Assoc. professor Emil Burtescu PhDUniversity of Piteşti
Abstract The fi nancial absorption of European funds in Romania can be
analyzed using a scenario simulated Monte Carlo method correlated with the
Solver method. The present article provides an original solution in response
to a structural questioning of the absorption approach in a concrete economic
context of anticipating the absorption of European funds in Romania during
the second multiannual budget term of the European Union (2014-2020). The
introduction synthesizes the concepts and methods exploited practically with
the help of a set of software packages, applied in an original manner, while
the main section of the article emphasizes the creativity or the innovativeness
of the correlative and structural solution off ered. Some fi nal remarks describe
the advantages of the correlative application of the scenario simulated Monte
Carlo method with the Solver method in a structural manner, anticipating the
absorption of EU funds.
Key words: simulation, scenario, Monte Carlo method, Solver
method, fi nancial absorption. JEL codes: C53, C58, E42, H43, H54, O22.
1. Introduction As René Descartes emphatically said in his Discours de la Méthode, in a specifi c manner that refers to mathematical reasoning, “nearly all things that come within the sphere of human knowledge are joined and concatenated in the same way”. An immediate requirement derived from that tenet is to validate and preserve the order of deduction of information from other information, as a support of a scientifi c method. The unpredictable eff ectiveness of Cartesian
methodological thinking can generate much more through multimethodology
Revista Română de Statistică - Supliment nr. 2 / 2019 115
or the multilateralism of methods used simultaneously (Livio, 2017), even
in a complex process of prospective fi nancial absorption of European funds.
This paper presents an original structural view of the absorption of European
funds by Romania in its second budget term as a member of the European
Union (2014-2020), optimistically correlating the scenario simulation based
on the Monte Carlo method with the Solver method, and capitalizing several
solutions in keeping with the Microsoft Excel packages (the Data Analysis/
Random Number Generation software), appreciated for its promptness and
interface in fi nancial simulations and modelling (Benninga, 2008), along with
the Eviews software package, used to determine descriptive statistics, the
results of the draws and the distributional and structural diagrams (Săvoiu,
2011; 2013), together with the innovative Microsoft Excel – Solver software,
applied in an innovative manner (Burtescu, 2010).
2. From optimized scenario simulation, based on the Monte Carlo
method, to the Solver method
In the 2014-2020 multiannual budget term, the prospect
of Romania’s fi nancial absorption of European funds represents a
methodological, computational, concerning the accurate and appropriate
foreseeing, and also the promptness in identifying and assessing the risks
of decreased absorption rates in the context of the implementation of the
projects that were approved and fi nanced.
In the multimethodic situation, following the combination of
scenario methods and the simulation methods, the contour of the possible
scenarios resulted from the views of the project management experts
(PM), ultimately correlating, after the simulation, in a prospective manner
based on a detailed structural anticipation at the level of the absorption
per program. The scenarios the could be capitalized on were pessimistic,
constant and optimistic, and this article refers only to the optimistic ones
resulting from the combination of PM experts’ views. Practically, the
classical brainstorming method was renounced, which capitalizes on PM
experts only to discern creative ideas or to harmonize their views, and the
technique of Delphi or Donald Phillips was capitalized on (Săvoiu et al,
2017; Tudoroiu, Săvoiu, 2018), out of the broad spectrum of specialized
techniques (Haefele, 1962).
In order to be able to predict eff ectively the fi nal rate and the
absorbed allocated funds from those that could be accessed, the two key
variables of the calibration simulation were calculated, or the initial rates
of the fi nancial absorption of the allocated funds (Fai) and of the fi nal
absorption rates (Rafi), adapted to the new allocation conditions, which
Romanian Statistical Review - Supplement nr. 2 / 2019116
were then rescenarized in keeping with the new views expressed, by
applying the Delphi technique (Botez, et al., 1989, Nicolae, Constantin,
Grădinaru, 1998). to a volunteer sample of 29 experts from 50 announced The fi nal data resulting from the Delphi technique, applied to the experts, were later taken over by the Monte Carlo simulation, being detailed for the optimistic scenario in table no. 1:
The probabilistic variables concerning the funds allocated (Fai) and the
fi nal absorption rates (Rafi), in the opinion expressed by PM experts
Table no. 1Variable (Fai) where
i=3 (billion€)
Resulting
probabilities
Variable (Rafi), where
i=5 (in coeffi cients)
Resulting
probabilities21.50 0.20 0.87 0.1022.40 0.50 0.90 0.1023.00 0.30 0.92 0.20
- - 0.95 0.30- - 0.98 0.30
Source: The data available online at http://www.fonduri-ue.ro/images/fi les/implementare-absorbtie/Anexa_1-Stadiul_ absorbtiei_2007_-_2013_martie_2017.pdf were reminded to PM experts, and their fi nal opinions are centralized and synthesized by authors.
As soon as the Monte Carlo method was ready for scenarizing and calibration, it was applied to a number of 10,000 draws, then to another of 20,000, and based on the fl uctuations between the values of maximum probability of €21.28 billion and €21.95 billion, and fi nally 30,000 draws were used, by means of the Microsoft Excel and the Data Analysis/Random Number Generation software packages. Finally, the application of the Monte Carlo method and the optimistic scenarization led to a prospective dominant value of the funds absorbed of €21.28 billion, which ultimately had the maximum probability of occurrence at the point values or a broader expected range described by [21.16 - 22.54] € billion, with a probability of 0.54. The optimistic scenarization leads to absorption rates ranging from [93.7% to 99.8%], and the dominat is a rate of fi nancial absorption of European funds to Romania of 94.6% (as maximum probability of occurrence
as a punctual value).
All these aspects are visible in the chart we fi nally made (in Figure no. 1), based on the Data Analysis/Random Number Generation software; the image resulted from a screen capture in running the Microsoft Excel program package:
Revista Română de Statistică - Supliment nr. 2 / 2019 117
Screen capture of optimized scenario simulation using the Monte Carlo
method with the Data Analysis/Random Number Generation software
Figure no. 1
�����D.�� �� ������ � �������������������- � ���� ������� ��������$!� �
�������� ����������
������ ���������� ���������� ����������� ����������� ���������� ����������� ����������� ����������� ���������� ����������� ����������� �����
������ ����������� �����
������ ��������� �����
Source: Data processed by the authors using the Microsoft Excel program package
For the descriptive statistical analysis of the Monte Carlo simulation
results, the EViews program package was also used, which is more appropriate
in this case to produce descriptive statistics on optimized scenario simulation
results and the normality of Kernel density distributions of the fi nal statistical
data series – as can be seen in Figure no. 2:
Distribution of the data series for the European funds that could be
absorbed in 2014-2020, optimistically scenarized and simulated by the
Monte Carlo method
Figure no. 2
European Absorbed Funds xi
Frequencyni
18,71 64819,35 62019,49 154019,78 123620,01 90820,16 145620,43 172520,61 297120,70 92021,07 181421,16 174821,28 446621,85 272621,95 445822,54 2764Total 30000
Source: The data of the Monte Carlo simulation were processed by the authors with the Eviews
software package
Romanian Statistical Review - Supplement nr. 2 / 2019118
The clarity, relevance and accuracy of the results of simulation using
the optimistically scenarized Monte-Carlo method are naturally infl uenced by
the structural composition by operational programmes, and it gets as low as the
project level, i.e. a greater complexity of the system of fi nancial absorption of European funds allocated generates a higher error, having eff ects similar to the
imprecision of the inaccuracy of the absorption probabilities deduced according
to the experts’ opinions…
The simulation of the phenomenon of fi nancial absorption of European funds by Romania, through the Monte Carlo method, in the situation of optimistic scenarizing generated by the opinions of PM experts (Săvoiu,
2006), fi nally also requires a correlation with the Solver method, in a creative or innovative manner, basically starting from the reality that there are various risks of decreasing the rate or correction in relation to the views of a number of experts (see the example of the Brexit risk, or of the diff erently geared
evolutions, which seem quite obvious in relation to overall prospects).
The Solver method, applied in a creative or innovative manner, is
exemplifi ed in a general model, focused on total European absorption funds and the limitations or constraints of the rate of this absorption (both variables being expressed in thousands of euros in fi nancial terms, and by absorption limits in promilles - 0/00 -), is displayed in two successive fi gures (Figure no. 3, at the level of an operational program or PO, and Figure no. 4, at the aggregate or totalizing level, in terms of accessed and absorbed funds, according to the two natural iterations: A. For any of the operational programs (POs), structured at project level:
Fictitious distribution of European projects reunited in an operational
program (PO), which are absorbed, scenarized optimistically and
simulated by the Solver method (fi rst iteration)
Figure no. 3.
Source: The data used by means of the Solver method are fi ctitious, and were processed by authors with the Microsoft Excel – Solver program package, modifi ed creatively or innovatively
Revista Română de Statistică - Supliment nr. 2 / 2019 119
B. At the aggregate level, quantifying the total absorbed funds detailed by
OP, with the clear possibility of anticipating developments in the second iteration
at program level, aggregated from projects, risks of failure, failed absorption,
other factors that induce decreases or increases rate of absorption, etc.
The fi ctitious distribution of the aggregate called European funds
absorbed by merging the operational programs (PO-1 … PO-6) that are
accessed and absorbed, optimistically scenarized, and simulated by the
Solver method (second iteration)
Figure no. 4
Source: The data used by means of the Solver method are fi ctitious, and were processed by
authors with the Microsoft Excel – Solver program package, modifi ed creatively or innovatively
Applying concretely the correlation with the Solver method to the
solutions of the simulation scenarized optimistically using the Monte-Carlo
method, three absorption variants are obtained, detailed at the level of:
i) six operational programmes (abbreviated by established acronyms)
in Figure no. 5
Romanian Statistical Review - Supplement nr. 2 / 2019120
The distribution of the European funds absorbed by the merging
of six accessed and absorbed operational programmes, scenarized
optimistically, and simulated by measn of the Solver method (after the
second iteration)
Figure no. 5
Source: The data used by means of the Solver method are fi ctitious, and were processed by
authors with the Microsoft Excel – Solver program package, modifi ed creatively or innovatively
ii) seven operational programmes (abbreviated by established
acronyms) in Figure no. 6
The distribution of the European funds absorbed by the merging of seven
accessed and absorbed operational programmes, scenarized optimistically,
and simulated by the Solver method (after the second iteration)
Figure no. 6
Source: The data used by means of the Solver method are fi ctitious, and were processed by
authors with the Microsoft Excel – Solver program package, modifi ed creatively or innovatively
iii) eight operational programmes (abbreviated by established
acronyms) in Figure no. 7
Revista Română de Statistică - Supliment nr. 2 / 2019 121
The distribution of the European funds absorbed by bringing together eight
accessed and absorbed operational programmes, scenarized optimistically,
and simulated by the Solver method (after the second iteration)
Figure no. 7
Source: The data used by means of the Solver method are fi ctitious, and were processed by
authors with the Microsoft Excel – Solver program package, modifi ed creatively or innovatively
Conclusions
The scenarized simulation by means of Monte Carlo method
correlated with the Solver method, modifi ed creatively or innovatively, brings
some favorable aspects, or application benefi ts, especially the promptness of
incorporating, into the foresight of fi nancial absorption, some emerging risks
that were not fully anticipated at the beginning, which virtually transform any
predictions in assessments of the future limited or aff ected by new constraints.
In addition to this major issue, the following benefi ts are obvious when
correlating the Monte Carlo scenario simulation method with the Solver method,
as a retrospective or post-calculus solution, as well as an effi cient prospective solution: a) it leads to a much faster and scenarized reassessment of data and risks; b) it lowers the level of anticipation down to that of the project with European funding accessed and absorbed (partially or totally in relation to their eff ective
absorption rate), and continues this operation at the level of the operational
programme; c) it promptly re-ranks risks, threats, limitations, restrictions, etc.
of the phenomenon of fi nancial absorption; d) it ensures immediate taking over
of changes in experts’ opinions on projects and operational programmes; e) it
provides immediate, or at least prompt solutions or relevant anticipations in the
case of funds blocking at the detailed project level, operational programme, and
subsequently, at aggregate or total level, concerning the fi nancial absorption of
European funds; f) it can also integrate structural elements, as well as linear
or nonlinear structural models, by capitalizing the Microsoft Excel – Solver
method with a high degree of coverage; g) it allows a broader integration of
opinions and scenarios at an aggregative and operational programme level; h)
the aggregate of total absorption, the total absorption rate is transformed by
correlating methods into an effi cient and realistic national retrospective and
Romanian Statistical Review - Supplement nr. 2 / 2019122
prospective working tool, and, in terms of anticipatory possibilities, it has a
decision-making impact related to truly signifi cant project management.
An example of the application presented in the paper gives – like the
correlational application of two methods simultaneously Monte Carlo – Solver
– originality and creativity, structurally and scenario-wise, pragmatically and
in a maximizing manner in respect to the level of absorption of European funds
by Romania during the 2014-2020 period, i.e. the second multiannual budget
term, in an aggregated and detailed manner, and also afterwards, even under
such circumstances as developing at diff erent speeds or rates (Câmpeanu,
2017) and stratifi ed convergence within the EU.
Bibliography
1. Decartes, R., 1990. Discurs despre metodă, București: Editura Academiei. 2. Livio, M., 2017. Este Dumnezeu matematician? București: Editura Humanitas. 3. Burtescu, E., 2010. Sisteme informatice în afaceri. Craiova: Editura Sitech. 4. Benninga, S. 2008. Financial Modelling, 3d ed, Cambridge, Massachusetts: MIT Press. 5. Săvoiu, G. 2013. Modelarea Economico – fi nanciară. Gândirea econometrică
aplicată în domeniul fi nanciar, Editura Universitară, Bucureşti.
6. Tudoroiu, L., Săvoiu, G., 2018. Prognosis, prediction, estimation, planning or
prospective of the absorption of European funds by Romania in the second budget
exercise as EU member state, In Progrese în teoria deciziilor în condiții de risc și incertitudine, Iași: Editura Perfomantica, vol. XXIX, pp. 195-204.
7. Haefele, J.W. 1962. Creativity and Innovation, New York: Reinhold
Publishing Corporation, Collection universallibrary. Contributor Universal Digital Library, pp. 53-56, [on-line] Available at: https://archive.org/details/creativityandinn010038mbp/ page/n5 [Accessed 26 December 2018]
8. Botez, M. (coord.), Dimitriu, P., Diaconescu, G.L., Draghici, M., Ladea, I., Priboi, T., Siletchi, M. 1989. Curs de prognoză, Centrul de Informare şi Documentare în Ştiinţele Sociale şi Politice (CIDSP), Bucureşti: Laboratorul de Cercetări Prospective al Universităţii
9. Nicolae, V., Constantin, L., D., Grădinaru, I. 1998. Previziune și orientare
economică, București: Editura Economică 10. Săvoiu, G., Burtescu, E., Dinu, V., and Tudoroiu, L. 2017. A Monte Carlo method
simulation of the European Funds that can be accesed by România in 2014 –
2020. E+M. Ekonomie a Management = Economics and Management, vol. 20(3) pp. 19-35. Available on line at: https://dx.doi.org/10.15240/tul/001/2017-3-002DOI:10.15240/ tul001/2017-3002, [Accesed 12 January 2019]
11. Săvoiu, G., Tudoroiu, L., Burtescu, E., 2017. Using the Monte Carlo Method to estimate the European funds absorbed by the Romanian economy from the EU in 2007-2013, Romanian Statistical Review Supplement, vol. 3, pp. 110-119. [online] available at <http://www.revistadestatistica.ro/supliment/wp-content/uploads/2017/ 03/A05_rrss_03 2017 _EN1.pdf > [Accesed 2 December 2018]
12. Săvoiu, G., 2011. Econometrie, Bucureşti: Editura Universitară
13. Săvoiu, G., 2006. Proiecte cu fi nanțare externă, Pitești: Editura Independența Economică 14. Câmpeanu, C., 7.03.2017 Ce viitor pentru Europa? Mai multe viteze, mai multe
direcții, disoluție, Revista 22, București. Available online at: https://revista22.ro/opinii/cristian-campeanu/ce-viitor-pentru-europa-mai-multe-viteze -mai-multe-direcii-disoluie [Accesed 1 December 2018]